Displaying similar documents to “Zeros of bounded holomorphic functions in strictly pseudoconvex domains in 2

A boundary cross theorem for separately holomorphic functions

Peter Pflug, Viêt-Anh Nguyên (2004)

Annales Polonici Mathematici

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Let D ⊂ ℂⁿ and G m be pseudoconvex domains, let A (resp. B) be an open subset of the boundary ∂D (resp. ∂G) and let X be the 2-fold cross ((D∪A)×B)∪(A×(B∪G)). Suppose in addition that the domain D (resp. G) is locally ² smooth on A (resp. B). We shall determine the “envelope of holomorphy” X̂ of X in the sense that any function continuous on X and separately holomorphic on (A×G)∪(D×B) extends to a function continuous on X̂ and holomorphic on the interior of X̂. A generalization of this...

Some properties of Reinhardt domains

Le Mau Hai, Nguyen Quang Dieu, Nguyen Huu Tuyen (2003)

Annales Polonici Mathematici

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We first establish the equivalence between hyperconvexity of a fat bounded Reinhardt domain and the existence of a Stein neighbourhood basis of its closure. Next, we give a necessary and sufficient condition on a bounded Reinhardt domain D so that every holomorphic mapping from the punctured disk Δ * into D can be extended holomorphically to a map from Δ into D.

Holomorphic series expansion of functions of Carleman type

Taib Belghiti (2004)

Annales Polonici Mathematici

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Let f be a holomorphic function of Carleman type in a bounded convex domain D of the plane. We show that f can be expanded in a series f = ∑ₙfₙ, where fₙ is a holomorphic function in Dₙ satisfying s u p z D | f ( z ) | C ϱ for some constants C > 0 and 0 < ϱ < 1, and where (Dₙ)ₙ is a suitably chosen sequence of decreasing neighborhoods of the closure of D. Conversely, if f admits such an expansion then f is of Carleman type. The decrease of the sequence Dₙ characterizes the smoothness of f. ...

Extension and restriction of holomorphic functions

Klas Diederich, Emmanuel Mazzilli (1997)

Annales de l'institut Fourier

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Strong pathologies with respect to growth properties can occur for the extension of holomorphic functions from submanifolds D ' of pseudoconvex domains D to all of D even in quite simple situations; The spaces A p ( D ' ) : = 𝒪 ( D ' ) L p ( D ' ) are, in general, not at all preserved. Also the image of the Hilbert space A 2 ( D ) under the restriction to D ' can have a very strange structure.

Analytic cohomology of complete intersections in a Banach space

Imre Patyi (2004)

Annales de l’institut Fourier

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Let X be a Banach space with a countable unconditional basis (e.g., X = 2 ), Ω X an open set and f 1 , ... , f k complex-valued holomorphic functions on Ω , such that the Fréchet differentials d f 1 ( x ) , ... , d f k ( x ) are linearly independant over at each x Ω . We suppose that M = { x Ω : f 1 ( x ) = ... = f k ( x ) = 0 } is a complete intersection and we consider a holomorphic Banach vector bundle E M . If I (resp. 𝒪 E ) denote the ideal of germs of holomorphic functions on Ω that vanish on M (resp. the sheaf of germs of holomorphic sections of E ), then the sheaf cohomology groups...

Variations of complex structures on an open Riemann surface

M. S. Narasimhan (1961)

Annales de l'institut Fourier

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Soit U 1 un ouvert dans C m . Soit π 1 : S U 1 une famille holomorphe de structures complexes sur une surface de Riemann non-compacte M , avec S t 0 = π 1 - 1 ( t 0 ) = M . ( S = S ( M × U 1 ) est une structure complexe sur le produit différentiable M × U 1 ). Soit M 1 un domaine relativement compact dans M . On démontre : pour tout voisinage de Stein U de t 0 , assez petit, la famille π 1 : S ( M 1 × U ) U est isomorphe à la famille π : Ω π ( Ω ) , où Ω est un de la variété produit M × C m , π étant la projection M × C m C m . On donne aussi un résultat analogue pour le cas des variations différentiables. ...

Analytic extension from non-pseudoconvex boundaries and A ( D ) -convexity

Christine Laurent-Thiébaut, Egmon Porten (2003)

Annales de l’institut Fourier

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Let D n , n 2 , be a domain with C 2 -boundary and K D be a compact set such that D K is connected. We study univalent analytic extension of CR-functions from D K to parts of D . Call K CR-convex if its A ( D ) -convex hull, A ( D ) - hull ( K ) , satisfies K = D A ( D ) - hull ( K ) ( A ( D ) denoting the space of functions, which are holomorphic on D and continuous up to D ). The main theorem of the paper gives analytic extension to D A ( D ) - hull ( K ) , if K is CR- convex.

On the Rogosinski radius for holomorphic mappings and some of its applications

Lev Aizenberg, Mark Elin, David Shoikhet (2005)

Studia Mathematica

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The well known theorem of Rogosinski asserts that if the modulus of the sum of a power series is less than 1 in the open unit disk: | n = 0 a z | < 1 , |z| < 1, then all its partial sums are less than 1 in the disk of radius 1/2: | n = 0 k a z | < 1 , |z| < 1/2, and this radius is sharp. We present a generalization of this theorem to holomorphic mappings of the open unit ball into an arbitrary convex domain. Other multidimensional analogs of Rogosinski’s theorem as well as some applications to dynamical systems are...